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Semi-active vibration control in cable-stayed bridges under the condition of random wind load

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2014 Smart Mater. Struct. 23 075027

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Semi-active vibration control in cable-stayedbridges under the condition of randomwind load

G Heo and Jeon Joonryong1

Konyang University, Civil and Environmental Engineering Department, Korea

E-mail: heo@konyang.ac.kr and jrjeon@konyang.ac.kr

Received 23 October 2013, revised 20 March 2014Accepted for publication 27 March 2014Published 12 June 2014

AbstractThis paper aims at an experimental study on the real-time vibration control of bridge structuresusing a semi-active vibration control method that has been in the spotlight recently. As structuresare becoming larger and larger, structural harmful vibration caused by unspecified externalforces such as earthquakes, gusts of wind, and collisions has been brought to attention as animportant issue. These harmful vibrations can cause not only user anxiety but also severestructural damage or even complete failure of structures. Therefore, in view of structural safetyand economical long-term maintenance, real-time control technology of the harmful structuralvibration is urgently required. In this paper, a laboratory-scale model of a cable-stayed bridgewas built, and a shear-type MR damper and a semi-active vibration control algorithm (Lyapunovand clipped optimal) were applied for the control of harmful vibration of the model bridge, inreal time. On the basis of the test results, each semi-active control algorithm was verifiedquantitatively.

Keywords: semi-active vibration control, MR damper, Lyapunov control, clipped-optimalcontrol, cable-stayed bridge

(Some figures may appear in colour only in the online journal)

1. Introduction

Lately, highly efficient large-scale structures in which highlydeveloped civil engineering, architecture, machinery, elec-tricity, electronic engineering, control system, IT, computer-ized numerical analysis and programming technology arecomplexly considered are appearing competitively in variouscountries, and this trend is expected to continue in the future.In particular, in the case of large-scale cable-stayed bridges acolossal amount of capital and effort is being invested latelyso as to reflect aesthetic sensibility, not to mention structuralsafety and functional usability, particularly in rising nationssuch as China. In the meantime, such large-scale cable-stayedbridges are structurally flexible and low in frequency anddamping capacity, so they are vulnerable to unexpectedexternal inflictions such as earthquakes and blasts, and thus

require measures to secure their structural safety and dur-ability [3].

On one hand, structurally harmful vibrations of bridgesare generated mostly by earthquake load, rain/wind load andcontinuous traffic load, when it is presumed that the initialdesign and construction had no flaws [1]. Thus, in order tosolve the problem of structurally harmful vibration of bridges,structures have been chiefly designed with an emphasis onsolidity and less flexibility [2], which costs more money andeffort. Consequently, a new countermeasure against harmfulvibration was required with more economy and usability, andafterwards methods were introduced to control vibrationrather than avoid it. Typical vibration control methods includepassive, active, semi-active and other complex controlmethods, and each of these methods uses a particular controldevice [3]. In particular, the active and semi-active controlmethods in comparison to the passive control method can beexpected to have highly effective control of vibration in that

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1 Author to whom any correspondence should be addressed.

they calculate the appropriate controlling power by obtainingand utilizing structural information in real time and givingthis controlling power directly to structures [4]. However,they are limited in terms of usability. Furthermore, activevibration control technology has technological limitations inthe aspect of effective vibration control in that it requires highinitial installation cost and generally large power supply. Inlight of this, a vibration control method with a new conceptsuitable for bridges was required, and in recent years a semi-active type of vibration control technology using the smartmaterial MR fluid has stood out as a new alternative [5, 6].

As for the semi-active vibration control technology, afterthe MR fluid that Carlson [4] and others had developed inLord Corporation in the USA in the 1990s was introducedinto the field of construction, many researchers includingSpencer [7] and Dyke [1] conducted studies of controlmethods using MR fluid devices. In line with this, Soong [3]and others put forward the possibilities of this semi-activevibration control technology realizing economical and effi-cient control while overcoming limitations of the existingpassive and active control methods, and also developed arelated control device and operation system, and conducted astudy on examples of application to actual structures. Figure 1shows real examples of cable-stayed bridges where vibrationis being controlled by means of semi-active vibration controltechnologies. Semi-active vibration control devices such asMR dampers can be used in real time for a field cable-stayedbridge, as seen in examples such as the Yellow River High-way Bridge (China, 2003) [27], Dongting Bridge (China,2002) [28], Eiland Bridge (the Netherlands, 2005) [29] andDubrovnik Bridge (Croatia, 2006) [30].

In particular, Spencer [7], Dyke [1] and others developedand proposed a dynamic model for simulating hystereticbehavior of MR dampers using MR fluid as well as a semi-active control algorithm for operating MR dampers, and alsoperformed an experimental study along with the numericalverification of this. Moreover, in Japan, Sodeyama [8, 9] andothers developed a high-capacity MR damper in the form of abypass and evaluated the performance of the MR damper byusing the dynamic model which had been proposed earlier bySpencer [7] and Dyke [1]. However, the control device uti-lizing MR fluid in the preceding study, in spite of its variousadvantages, has the problem of insufficient initial reaction

under sudden external load as a result of precipitation ofcarbon powder contained in the MR fluid as well as theproblem of surplus stress generated due to the magnetizationof the electromagnet; therefore, continuous studies arerequired. Additionally, an appropriate control algorithm isnecessary in order to utilize the aforementioned MR-fluid-based damper for vibration control. In line with this, Spencer[7] and Dyke [1] not only investigated mechanisms of the MRdamper but also cleared up and proposed various semi-activecontrol algorithms so as to make use of the mechanism; theyalso verified its validity through numerical and experimentalverification.

As stated above, in the global circumstances whereanalytical and experimental studies on semi-active vibrationcontrol of bridges are actively performed, especially in theUSA and Japan, existing studies in Korea were limited to thedevelopment of certain MR control devices and the verifica-tion of control algorithms [10, 11, 18, 19]; even then, thosestudies were focused on architectural structures such asbuildings. In contrast, the issue of vibration control in bridgesis mainly dealt with in terms of numerical analysis [12]; otherthan that, studies on cable, vibration control in bridges [13]were narrowly conducted. Nevertheless, in these studies,vibration control effects were assessed using existing randomseismic waves such as El Centro and Kobe waves, etc; as forcable vibrations, as they are sensitive to wind load, com-plementary studies need to be carried out side by side, con-sidering the wind load conditions in the real system. Inparticular, with the example of the collapse of the TacomaNarrows Bridge in Seattle taken into consideration, studiesshould certainly be conducted on the control of harmfulvibration induced by dynamic wind load in large-scalebridges in Korea, because Korea has the geographic and cli-matic characteristics of typhoons that accompany heavy rainand gales [14, 15] concentrated between July and Septembereach year [16, 17].

In this paper, on account of the necessity of effectivelymanaging and controlling the harmful vibration induced bywind load, we aim to perform an experimental study on real-time vibration control for cable-stayed bridges that haverelatively flexible structural properties. For the experiment, anexperimental structure is constructed by reducing and mod-eling Seohae Grand Bridge, which is a representative Korean

Smart Mater. Struct. 23 (2014) 075027 G Heo and J Joonryong

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Figure 1. Examples of semi-active vibration control in real time for a field cable-stayed bridge. (a) Yellow River Highway Bridge. (b)Dongting Bridge. (c) Eiland Bridge. (d) Dubrovnik Bridge.

cable-stayed bridge, and then external harmful vibrationconditions are simulated by reproducing the wind loadacquired from the actual bridge through adjustment to thescale of the experiment. In addition, in order to apply thesemi-active control method that hss recently been highlightedto the experiment, a shear-type MR damper is designed andproduced by ourselves, and a control system is completed forthe experiment by applying semi-active control algorithmssuch as Lyapunov and clipped optimal that have been verifiedin precedent studies. Then, the MR damper that is developedassesses the dynamic range and maximum possible control-ling power in dynamic load tests experimentally. Last, thevibration control effects of the two semi-active vibrationcontrol strategies on the random vibrations occurring inbridges are assessed quantitatively by utilizing the controlperformance index (J ) for the target position displacement,acceleration and power consumption in the operation of MRdampers. Finally, we present the possibility of the vibrationcontrol system and control strategy constructed in this paperbeing utilized for controlling and managing in real time ran-dom vibration loads that are regular or unexpected, includingthe wind load occurring in actual bridges in the future; fur-thermore, data of conditional experimental research on thesemi-active vibration control system for cable-stayed bridgesare provided.

2. Semi-active control device

2.1. Determination of capacity for a shear-type MR damper

In this paper, the maximum external force occurring instructures is calculated against the external excitation signalsused in the vibration control experiment in order to determinethe capacity of the controlling device, and the capacity of theshear-type MR damper is determined so as not to exceed thecalculated maximum external force. First of all, the externalexciting force for vibration control was obtained from theunexpected wind load condition which occurred approxi-mately between 11.20 and 11.30 in the evening of 27 Feb-ruary 2011 on Seohae Grand Bridge in South Korea, which isillustrated in figure 2(a); the vertical acceleration responses atthe central reinforced body on the middle span of the cable-stayed bridge were acquired for the duration of 50 s for use.At this time, the maximum wind velocity was approximately15 m s−1, and the maximum acceleration was approximately0.01 g. Then, in order to calculate the maximum externalforce which occurred in the model structure under the above-mentioned external excitation condition, first the accelerationand displacement response occurring in the location where theshear-type MR damper will be attached are experimentallyacquired as in figures 2(b) and (c); and then the maximumacceleration, velocity and displacement response at the timeare calculated as in table 1, which are used to calculate theinertial force, damping force and strength of stability, shownin table 2. In this calculation, the mass, damping and rigidityused for calculation were calculated through the analysis offrequency of response acceleration based on the first bending

mode, and last a total generation force of approximately140 N was identified from the excitation of wind load on themodel cable-stayed bridge. At this time, in consideration ofthe fact that the controlling capacity of the MR damper cannotexceed the total calculated generation force, the capacity ofthe MR damper is determined at the level of 10 N by using thefollowing equation, so that the controlling power is set ataround one-tenth of the total generation force.

η τ= + = +η τF F F HSA

gA( ) . (1)y

Here, F is the controlling power of the entire shear-typeMR damper, ηF is the viscosity controlling power arising from

the viscosity of the MR fluid, τF is the magnetism controllingpower resulting from current injection, H is the strength of themagnetism, η is the plastic viscosity of the fluid, S is therelative velocity of stimulation, τy is the yielding stress of the

applied MR fluid, A is the area of the plate where the mag-netism is applied, and last, g is the gap of the flow path.

2.2. Design of the shear-type MR damper

Generally, one of the material properties of MR fluid usedhere is the ability to control the stress of the MR fluid, that canbe affected by the generated magnetic field by adjusting theintensity of the current being injected; therefore, if the currentis increased, the control stress of the MR fluid is expected tobe enhanced [20]. In this paper, as a shear-type MR damper, ahydro-carbon type MRF-132DG, made by Lord, was used.Also, considering that magnetic saturation and annealing aremaximized when steel is closest to pure iron, which contains avery small amount of carbon, the electromagnet yoke andshear plate were produced with low carbon steel of aroundS15C–S20C so that the shear-type MR damper has max-imized control performance. Finally, the connecting rod of thefront boards and its external cover were made of aluminum sothat the magnetic field would not be affected, entirelyfocusing on the front board. The shear-type MR damperproduced with the above-mentioned design conditions isshown in figure 3. The produced shear-type MR damper hasan electromagnet which was produced by winding an enamelcoil 0.4 mm in diameter around the yoke 2000 times; then, thegap between the yoke and the wear plate was set at 6 mm onthe left and right alike. Between the shear plate and the wearplate was inserted a sponge impregnated with MRF-132DG tocomplete the control device, and RD-3002-03, the currentdriver provided by Lord Corporation [20], was used for thepurpose of stable supply of current.

In this paper, our decision on control capacity and thekind of controller was made with consideration of maximumvibration load inflicted on the mid-span of the model cable-stayed bridge. A linear MR damper made by Lord Corpora-tion was not suitable for our model of the bridge because ofits excessive control capacity, so we designed and manu-factured a shear type of MR damper. However, both shear andlinear types of MR damper work on the same principle of the

Smart Mater. Struct. 23 (2014) 075027 G Heo and J Joonryong

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carbon chain’s cohesive force in the MR fluid, while eachshear mode and valve mode work differently as in figure 4.

2.3. Dynamic load test of the shear-type MR damper

In the preceding section 2.2, a MR damper was designed andproduced in a shear type for controlling vibration. In thissection, a dynamic load experiment is carried out with variousexperimental conditions so that the controlling performanceof the shear-type MR damper can be quantitatively assessed.In particular, the controlling performance of a semi-activeMR damper is indicated by performance evaluation indicessuch as controlling power and dynamic range on the basis ofthe minimum generation controlling power during the off-state of the input current as well as the maximum generationcontrolling power during the on-state of the input current.

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Figure 2 Responses from real and model cable-stayed bridges. (a) Selected acceleration (real). (b) Vertical acceleration (model). (c) Verticaldisplacement (model).

Table 1. Maximum response of model bridge to excitation.

Kinds ofresponse

Acceleration(m s−2)

Velocity(m s−1)

Displacement(m)

Maximumresponse

4.3122 0.1255 0.0036

Table 2. Maximum force of model bridge with excitation.

Kinds offorce

Inertiaforce (N)

Dampingforce (N)

Restoringforce (N)

Maximumforce

139 3.61 0.74

First, the controlling power Fc can be expressed as the fol-lowing equation. Here, Fc max is the maximum generationcontrolling power, and Fc min is the minimum generationcontrolling power.

= +F F F . (2)c c cmax min

Next, the dynamic range, which is the second evaluationindex, is important for a semi-active control device; Carlson[4] and others present the dynamic range of a semi-activecontrol device from 1 to 20. These dynamic ranges can beexpressed as ratios relative to the maximum and minimumgeneration controlling power that has been calculated fromthe above equation (2), and when such dynamic ranges areexpressed in the following equation.

=F

FDR . (3)c

c

max

min

Last, as for the experimental table setup for a dynamicload experiment, an exciter with a maximum displacementcapacity of ±1.0 inch was utilized in order to generate forcedshear plate movement in the MR damper, and a commercialmodal measuring tool (T-DAS) was used to operate an exciterfor different exciting frequencies. In addition, a tension–-compression load cell (DBBP-500) was used to measure thegenerated controlling power, and an LVDT (CDP-50) with anoverall stroke capacity of 50 mm was used to measure thegenerated displacement of the damper. At this time, for theorganization of the measuring system, a dynamic data logger

(DRA-107 A) was used to acquire data from a measuringdevice, and the data were acquired for the duration of 40 s foruse with a sampling cycle of 0.01 s. Conditions for thedynamic load experiment were largely divided into changes inexcitation velocity and excitation frequency; for each condi-tion, the intensity of input current was set as off (0 A) and on(2 A). First, in relation to the change of excitation velocity,when a sine wave of 1 Hz was given for excitation with thelaboratory conditions taken into account, velocity conditionsof 5, 10, 15, 20, 25, 30, 35 and 40 mm s−1 were respectivelygiven to the dynamic load experiment. As seen in figure 5 andtable 3, a representative force–displacement trajectory curveand result values are obtained. Moreover, as for the change ofexcitation frequency, under the velocity condition of 40mm s−1 with a modal exciter, sine waves of 1, 2, 3, 4 and 5 Hzwere given respectively, whose force–displacement trajectorycurve and result values are shown in figure 6 and table 4.

When we examine figures 5 and 6, the controlling powerof the MR damper is observed to change in accordance withthe change of velocity or frequencies using a certain excita-tion wave form. It is also shown to change along with thechange of input current. Therefore, our MR damper is foundto operate normally, and it was identified that the change ofexcitation velocity rather than that of excitation frequencycontrolled the change of the generated controlling power, andeventually the excitation velocity turned out to be the primarydesigning element that influences the generated controllingpower.

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Figure 3. Prototype of the shear-type MR damper.

Figure 4. Comparison of shear and linear types of MR damper.

Next, if we examines tables 3 and 4, the shear-type MRdamper in this paper showed the minimum generation controlpower of around 3.88–4.28 N on average in the off-state ofthe input current; in the on-state of the input current, it

displayed the maximum generation control power of around10.67–11.86 N on average. As a result of this, the controllingpower was identified to be approximately 6.79–7.58 N onaverage, and the dynamic range calculated here turned out to

Smart Mater. Struct. 23 (2014) 075027 G Heo and J Joonryong

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Figure 5. Cases of displacement–control power hysteresis loop against velocity. (a) 1 Hz, 10 mm s−1. (b) 1 Hz, 20 mm s−1. (c) 1 Hz,30 mm s−1. (d) 1 Hz, 40 mm s−1.

Table 3. Cases of control power, controllable force and dynamic range against velocity.

Velocity (mm s−1)

1 Hz 5 10 15 20 25 30 35 40 Average

Passive off (0 A) force (N) 3.266 3.513 3.593 3.986 4.256 4.303 4.420 3.766 3.88Passive on (2 A) force (N) 8.953 9.973 10.453 10.973 10.800 10.963 11.576 11.740 10.67Controllable force (N) 5.686 6.460 6.860 6.986 6.543 6.660 7.156 7.973 6.79Dynamic range 2.74 2.83 2.90 2.75 2.53 2.54 2.61 3.11 2.75

be approximately 2.75–2.77. Consequently, the shear-typeMR damper in this paper, rather than having high-performingcontrol power, was verified to be valid as a semi-activecontrol device that can generate controlling power by chan-ging the input current in the vibration control experiment.

2.4. Dynamic modeling of the shear-type MR damper

In order to investigate the dynamic behavior of the developedshear-type MR damper numerically, in this paper the powermodel and Bingham model, of which the practical aspect is

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Figure 6. Cases of displacement–control power hysteresis loop against frequency. (a) 2 Hz, 40 mm s−1. (b) 3 Hz, 40 mm s−1. (c) 4 Hz,40 mm s−1. (d) 5 Hz, 40 mm s−1.

Table 4. Cases of control power, controllable force and dynamic range against frequency.

Frequency (Hz)

40 mm s−1 1 2 3 4 5 Average

Passive off (0 A) force (N) 3.766 4.263 4.463 4.573 4.346 4.28Passive on (2 A) force (N) 11.740 12.250 11.433 11.833 12.075 11.86Controllable force (N) 7.933 7.986 6.970 7.260 7.728 7.58Dynamic range 3.11 2.87 2.56 2.58 2.77 2.77

considered, among various dynamic models are adopted.First, the power model can be applied simply in order toexpress the dynamic behavior of the viscous fluid damper byutilizing the force–velocity relation [8, 9]. The force–velocityrelations in this power model are expressed as in equation (4).Here, F is the overall control power of the MR damper, Ci isthe nonlinear damping coefficient,V is the piston speed of thedamper, and last n is the index. From the basic assumption,variables Ci and n are independent of the amplitude and fre-quency, and these variables are determined by the least squareerror method between the experimental value and the ana-lyzed value. In addition, even when n converges to zero, thereremains some damping force within the designated limit; thusit can be used to simulate behaviors of the MR damper.

=F C V . (4)in

Next, the Bingham model is one of the representativedynamic models for simulating the dynamic behaviors of MRdampers [21, 22]. Here, the damping device (dashpot) and thefriction device (Coulomb friction slider) are regarded as beingconnected in parallel with each other; in this case, the for-ce–velocity relations in this Bingham model are expressed asin equation (5). Here, F is the overall control power of thedamper, V is the piston speed of the damper, C0 is thedamping coefficient, and last FF is the friction force. Both ofthese models can be effective in simulating the properties ofdynamic behaviors of MR damping devices numerically, asboth of them have simple relational expressions and out-standing performance.

= +F F V C Vsgn ( ) . (5)F 0

In this paper, in order to understand the tendency ofnumerical simulation in each dynamic model, dynamicmodeling was conducted considering the passive off (0 A)condition and passive on (2 A) condition in the experimentalresults that are illustrated in table 3; parameters for eachdynamic model that have been identified are shown in table 5.Then, the control power, controllable power, dynamic rangeetc of the power and Bingham models that have been pre-dicted with the dynamic model variables identified in table 5against each velocity are represented in table 6. Finally, theanalyzed values against the experimental values for a 2 Acondition of 1 Hz are represented in figure 6 so as to evaluatethe control power that has been predicted from each dynamicmodel.

First of all, in table 6 and figure 7(a), it was verified thatthe Power model considers the plastic properties appearingafter the yield of MR fluid to have nonlinear behaviors that

are similar to the actual behaviors of the fluid so as to simulatedynamic behavioral properties of the MR damping devicemore efficiently. In addition, as shown in table 6 andfigure 7(b), a predicted model, which is based on the Binghamlinear model, turns out to be slightly different from theexperimental data. Therefore, the two dynamic models eval-uated in this paper are evaluated to be effective in simplemodeling that can consider the dynamic behaviors of the MR-fluid damping device as nonlinear and linear, and the shear-type MR damper in this paper is experimentally and analy-tically proved to be valid as a semi-active control device.

3. SEMI-active control algorithm

3.1. Lyapunov control algorithm

A M Lyapunov (1893) in Russia presented a general theoryon system stability, which is used as the most general methodfor judging stability of all the systems to date. Thus, theLyapunov stability-based control approach was chosen indesigning a feedback control device for structure vibration[23]. Leitmann [24] and others applied the Lyapunov directapproach to design a semi-active control device, and thecontrol law determined then is the following:

= −( )v V H z PB f( ) . (6)iT

i imax

Here, ⋅H ( ) is a Heaviside step function, which limitsthe size of the voltage injected into the MR damper, the semi-active control device, to 0 and Vmax; the subscript i is anexpression for considering the number of control deviceswhen multiple control devices are in use; vi is the controlvoltage that needs to be entered into each control device at thecurrent phase, Bi is the ith column of the B matrix that has thesame number of columns as that of the control devices shownin the initial state equation; f

iis the control power generated

and observed from the ith control device in the previousphase, and lastVmax is the maximum voltage that needs to flowinto the control device according to the limit conditions of thecontrol device in the current phase.

3.2. Clipped-optimal control algorithm

Along with the semi-active control strategy using Lyapunovcontrol theory, Dyke [25, 26] and others presented theclipped-optimal control algorithm as a semi-active controlstrategy using MR dampers. The basic concept of theclipped-optimal control algorithm calculates the controlpower ( f

ci) required of the MR damper by using the control

power ( f ) and response (y) from the structure as well as thedesigned linear-optimal controller K S( )c . Therefore, in theforce-feedback loop, the force f

igenerated from the MR

damper needs to be in approximate conformity with therequired optimum control power f

ci. As a result, the control

rule that has been determined so that the force generatedfrom the MR damper f

icomes close to the required optimal

Smart Mater. Struct. 23 (2014) 075027 G Heo and J Joonryong

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Table 5. Model parameters of shear-type MR damper.

Power model Bingham model

Current(A)

Ci (N(mm s−1)−1) n

C0 (N(mm s−1)−1) FF (N)

0.0 2.6569 0.1279 0.0248 3.32882.0 7.4545 0.1213 0.0687 9.1316

control power fciis the following:

= −( ){ }v V H f f f . (7)i i i imax c

Here, when the MR damper provides the required control

power =( )f fci i

, voltage signals should be injected into the

MR damper so as to show the control power that conforms tothe state. If the control power from the MR damper is weakerthan the required power, and the two powers have the samesign, the maximum voltage is sent to the current amplifier sothat the control power of the MR damper shows the maximumcontrol power that corresponds to the required control power.

For the rest of the cases, the signal 0 is sent to the MRdamper.

3.3. Performance index of vibration control

Generally, the amplitude representing the size of the vibrationcan be quantified as peak values, peak to peak values, averagevalues, RMS values, etc In this paper, with reference to thevibration control performance index used by Jansen [5] andothers in the benchmark on the cable-stayed bridge vibrationcontrol as well as to the above quantifying method forvibration amplitude as evaluation indexes, the peak value forassessing the momentary size of vibration and the RMS value

Smart Mater. Struct. 23 (2014) 075027 G Heo and J Joonryong

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Figure 7. Cases of displacement–control power hysteresis loop against frequency. (a) Power model prediction (1.0 Hz, 1.25 mm sinusoidaldisplacement excitation, 2.0 A). (b) Bingham model prediction (1.0 Hz, 1.25 mm sinusoidal displacement excitation, 2.0 A).

Table 6. Analysis results of Power and Bingham models.

Velocity (mm s−1)

Dynamic modeling for MRdamper 5 10 15 20 25 30 35 40 Average

Predict (0 A) Force (N) Power 3.264 3.566 3.756 3.897 4.010 4.104 4.186 4.258 3.83Bingham 3.453 3.577 3.701 3.825 3.949 4.073 4.197 4.321 3.89

Predict (2 A) Force (N) Power 9.062 9.856 10.353 10.720 11.015 11.261 11.473 11.661 10.53Bingham 9.475 9.819 10.162 10.506 10.849 11.193 11.536 11.880 10.68

Predict controllable force (N) Power 5.798 6.290 6.597 6.823 7.005 7.157 7.287 7.403 6.71Bingham 6.022 6.242 6.461 6.681 6.900 7.120 7.339 7.559 6.79

Predict dynamic range (Dr) Power 2.78 2.76 2.76 2.75 2.75 2.74 2.74 2.74 2.75Bingham 2.74 2.75 2.75 2.75 2.75 2.75 2.75 2.75 2.75

for assessing the amount of energy for the duration of theinterested time are chosen for evaluation. The vibrationcontrol performance indexes used here are absolute maximumdisplacement (J1), RMS displacement (J2), absolute maximumacceleration (J3), RMS acceleration (J4), consumption of inputvoltage (J5), etc, and the formulaic expressions of these per-formance indexes are as in table 7.

Here, xd,max is the maximum displacement response in a

non-controlled state, xid is the displacement response for each

time phase, xd,RMS is the RMS displacement response in a non-

controlled state, xid,RMS is the RMS displacement response for

each time phase, xa,max is the maximum acceleration responsein the non-controlled state, xi

a is the acceleration response for

each time phase, xa,RMS is the RMS acceleration response in anon-controlled state, xi

a,RMS is the RMS acceleration responsefor each time phase, Vi is the input voltage in a control statebased on Lyapunov or clipped-optimal control strategy, andVon is the full input voltage in a passive-on state. Among thevibration control performance indices considered in thispaper, –J J1 4 can be useful in representing the effects ofvibration control as the change of vibration amplitude; inparticular, the vibration control performance index J5 can beused as a special performance index term that can be shown inan active or a semi-active control method.

4. FE modeling and modal test of model bridge

4.1. Design and production of cable-stayed bridge

A cable-stayed model bridge has been selected in this paper inorder to conduct an experimental study on vibration control.The second moment of area was reduced to the maximum sothat the bridge deck becomes sensitive to the vibration ofexternal force during the initial design of the bridge, and forconvenience material properties of table 8 were considered inthe construction of the FE model. Here, cable tension wasintroduced in the assembly of the model structure to consideronly the self-load effect of the superstructure throughout theentire section, and the superstructure of the model structurethat has been completed was made horizontal. For this

purpose, the self-load of the superstructure was assumed to beuniform, and the load was distributed in equal intervals ontothe floor beam of the superstructure, and then this load wasutilized as the tension force of the cable. Here, the load cellwas utilized to place the quantitative tensile force, and thecable tension was introduced by allotting the force ofapproximately 18 N per cable, and then the horizontality ofthe superstructure was checked by using the level aligner afterhaving completed the introduction of tension. Taking theorder of the tension introduction in an actual cable-stayedbridge as an example, the order of the cable tension intro-duction was to advance from the tower toward the outside,tension was introduced symmetrically left and right inconsecutive order, and the last introduction of tension wasconducted in the cable of the middle span. The model cable-stayed bridge for vibration control in which the aboveconditions are reflected is shown in figure 8.

4.2. FE analysis of cable-stayed bridge

In order to analyze the structural dynamic properties of theproduced model bridge, FE modeling-based numerical ana-lysis was conducted in this paper. For this purpose, I-DEASfrom UGS, a commercial structural analysis program, wasused; and a three-dimensional detailed FE model was orga-nized as in figure 9 by applying the physical properties oftable 8. Here, a 1D beam element was considered for thebridge deck and the tower of the structure, a rigid element wasconsidered for the bridge deck boundary conditions, a 1D rodelement was considered for cable; as for the floor beam andlumped mass, a 1 kg lumped mass was considered for each ofthe 39 nodes, which are the positions of the floor beams onthe area of the central bridge deck excluding the pylon andboth sides. Next, as for the boundary condition, a clamp wasconsidered for the substructure of the pylon, a roller wasconsidered for both sides of the superstructure and the right-side pylon connection, and a pin was considered for the left-side pylon connection. Last, as for the degree of freedomcondition of the structure, the DOF was given in the directionof the y axis with the 39 nodes on the central bridge deck asthe base to complete the 3D detailed FE model. In this con-text, the FE analysis of the model bridge considered a total oftwo lowest flection modes for the purpose of vertical vibration

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Table 7. Performance indexes of vibration control.

Absolute maximumdisplacement

RMSdisplacement

Absolute maximumacceleration

RMSacceleration

Consumption of the inputvoltage

= { }J maxx

x1id

d,max = { }Jx

x2id,RMS

d,RMS = { }J maxx

x3ia

a,max = { }Jx

x4ia,RMS

a,RMS= ∑

∑{ }J V

V5i

on

Table 8. Material properties of cable-stayed bridge.

Materialproperty

Modulus of elasticity(kgf mm−2)

Shear modulus of elasticity(kgf mm−2)

Poisson’sratio

Unit weight(kgf mm−2)

Yield strength(kgf mm−2)

Steel ×2.10 104 ×8.10 103 0.30 × −7.85 10 6 40

control, and the natural frequency and mode shape of themodel bridge, that has been analyzed with the Guyanreduction method applied, are as in figure 10.

4.3. Modal test of cable-stayed bridge

A modal experiment was carried out in this paper in order toanalyze the dynamic properties of the model cable-stayedbridge and to verify the validity of the FE model that had beenconstructed before. For this purpose, an HP-VXI 1432 wasused to measure the response signals from the structure, anddata were obtained and analyzed by utilizing T-DAS by MTS.In order to obtain acceleration responses of the structure, aDytran model 3134D was used for a total of 39 points on thebridge deck that had been selected at equal intervals. Inaddition, the central bridge deck was selected for the excitinglocation of the impact hammer for structure excitation, wherea Dytran model 5850A was used. Here, data were obtained byaveraging 30 times with the maximum response frequencyrange of 35 Hz, and the reference channel was set up with ahammer to obtain and analyze the FRF. The time responseand frequency response obtained here are as in figure 11, andthe natural vibration frequency and mode shape calculatedhere are as in figure 12. At this time, the 3D detailed FEmodel was analyzed and the modal experiment was con-ducted to compare natural frequencies as in table 9. In table 9,satisfactory results were gained, as the error rate of analysis

and experiment was proven to be approximately 1%. On thebasis of these results, the FE detailed model constructed inthis paper was verified to simulate the behavioral properties ofthe actual model structure sufficiently; therefore, it is con-firmed that the FE model constructed in this paper is valid.

5. Vibration control of model bridge

5.1. Programming of semi-active control algorithm

In this paper, a real-time integrated vibration control systemwas constructed by applying the two semi-active controlalgorithms, Lyapunov control and clipped-optimal controlmethods, which are representative of semi-active controlstrategies, and then an experimental study was conducted totry to control the vibration generated by random load on amodel bridge in real time. At the time, the weighting matrix(Q) of the Lyapunov equation, which needs to be carefullyconsidered in the Lyapunov control method, was determinedfrom the initial unit matrix (I ) with trial and error. Here, allthe basic information required for forming the control logic,such as dynamic parameters of the structure, sensitivity ofvarious sensors, source data of disturbance signal, andchannel set-up of reference response was coded in aMATLAB M-file and then loaded in the pertinent controlblock to be used. Finally, the block diagram of the Lyapunov

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Figure 8. Model bridge for vibration control.

Figure 9. FE modeling of model bridge using I-DEAS.

Figure 10. Results by FE analysis. (a) First bending mode (9.1719 Hz). (b) Second bending mode (11.2544 Hz).

control strategy formed by using MATLAB Simulink isshown as figure 13. Next, in the case of clipped-optimalcontrol, the control power calculated from the optimal controldevice is provided as an important index for deciding whetheror not there is control by comparing with the control power ofthe structure in the current state; therefore, it is an importantdesigning element for the optimal vibration control of thestructure, and here the weighting matrices (P) and (Q) arerequired to be decided. Thye can be properly chosenempirically in the same way as in the Lyapunov controlmethod; the effect of the signal noise is assumed to be verylittle in this paper, and both the matrices were determinedwith trial and error from the initial unit matrix (I ). Last, theblock diagram of the clipped-optimal control strategy formedby using MATLAB Simulink is shown in figure 14.

In this paper, in order to examine the control effect as aresult of the control rule formed above, the vibration controlpattern before and after the control was reviewed through

simulation. For this, the Bingham model was applied to theMR damper, and a control response of each control rule, incontrast to a non-controlled state, was evaluated schemati-cally as in figure 15. Here both the control rules showedsatisfactory patterns of vibration reduction.

5.2. Setup of semi-active vibration control test

In this paper, for the real-time vibration control experiment ofthe model cable-stayed bridge, structural responses wereobtained in real time from the structure; moreover, the inte-grated control system for handling in real time the controlsignals that have been generated using the obtained responseswas constructed as in figure 16. Here, an acceleration sensor(Dytran 3134D), a displacement sensor (Tokyo Sokki CDP-50), and a force sensor (Dytran 1051V5) were used. Theacceleration data obtained at this time are the referenceresponse for assessing the state of the structure, the obtaineddisplacement data are the reference response for determiningthe control effect along with the acceleration data at theposition where the control device is installed, and last theobtained force data are utilized as a response for calculatingthe control output by measuring the real-time control powerof the control device. In addition, the data logger, sinceresponse data are divided into static and dynamic data,commercial static and dynamic loggers such as the FYLDE379TA static logger and the Dytran 4123B amplifier werecombined for use so as to obtain both types of datum con-currently. Moreover, for the exciter, a modal exciter (FamtechEDS50-120) was installed at the central point of the left spanon the bridge, and a certain amplitude of vibration wasimposed on the structure; at this time, the vertical randomwaveform of the actual cable-stayed bridge which had beenadjusted in size considering the laboratory conditions wasutilized as an exciting wave form. Also, the dSPACECP1103, a real-time guaranteed I/O board, was utilized so asto connect the aforementioned hardware with a PC, which is auser environment. Finally, the response time of the shear typeMR damper was set to work less than 0.01 s at maximumwhile feedback controlling the vibration of the model cable-stayed bridge in real time. In order to determine the response

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Figure 11. Modal test results for model bridge.

Figure 12. Results of modal test. (a) First bending mode (9.0890Hz). (b) Second bending mode (11.2557 Hz).

Table 9. Comparison of analytical and experimental frequency.

Bendingmode

FE anal.results (Hz)

Exp.results (Hz)

Errorratio (%)

1st mode 9.1719 9.0890 0.91202nd mode 11.2544 11.2557 0.0115

time, I considered the response speed of MR fluid, also howlong it takes for the control algorithm to calculate and for thecontrol signals to the D/A to convert, by means ofexperiments.

The damper can be mounted in the mid-span of fieldbridges as in figure 17. It controls the vertical vibration with acontroller which is placed in the horizontal direction. Such atransition of control direction is in public use. So the way ofmounting the damper can be varied.

5.3. Results of semi-active vibration control test

The results of Lyapunov control on the displacement responseand acceleration response obtained from the central point ofthe bridge deck on the model bridge are illustrated infigure 18, while the results of clipped-optimal control arerepresented in figure 19. First of all, in the cases of the dis-placement response and acceleration response of figure 18,control effects were found to improve in the order of passive-off control, passive-on control, and Lyapunov control incontrast to a non-controlled state. Similarly, in the cases of thedisplacement response and acceleration response of figure 19,control effects were found to improve in the order of passive-off control, passive-on control, and clipped-optimal control incontrast to a non-controlled state. In addition, the distributionof input voltage consumption for each semi-active controlmethod is illustrated in diagram form in figure 20 andfigure 21. As shown here, it is clearly verified that

consumption of control voltage is greatly reduced when thevibration is controlled for 50 s in total.

6. Estimate of vibration control

In order to evaluate the performance of a vibration controlalgorithm through an experiment, the effects of vibrationcontrol were evaluated in this paper by selecting the peakvalue to assess the momentary size of vibration, the RMSvalue to assess the amount of energy for the time of interest,and the consumption rate of input voltage in the semi-activecontrol as in table 7. In this context, the vibration controlexperiment was carried out under the five experimental con-ditions in this paper; then the vibration control performanceindexes ( –J J1 5) were calculated by comparing the sizes ofresponses for each experimental condition, and finally controleffects for each experimental condition were evaluated andillustrated in table 10.

6.1. Evaluation of absolute maximum displacement

When we examine table 10 in relation to the generationmaximum displacement for each experimental condition, theresults are shown as approximately 3.64 mm in a non-con-trolled state, approximately 3.13 mm in a passive-off control,approximately 1.96 mm in a passive-on control, approxi-mately 1.72 mm in Lyapunov control, and approximately

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Figure 13. Simulink to Lyapunov control.

1.75 mm in a clipped-optimal control. When these arerepresented as absolute maximum displacement (J1), they areshown to be approximately 86.05% in a passive-off control,approximately 54.06% in a passive-on control, approximately47.28% in a Lyapunov control, and approximately 48.29% ina clipped-optimal control with the non-controlled state as thestandard. As for the control effects in relation to these figures,effects of vibration size reduction were gained as much asapproximately 13.95% in a passive-off control, approximately45.94% in a passive-on control, approximately 52.72% in aLyapunov control, and approximately 51.71% in a clipped-optimal control with the non-controlled state as the standard.

6.2. Evaluation of RMS displacement

When we examine table 10 in relation to the RMS displace-ment generated for each experimental condition, the resultswere approximately 0.49 mm in a non-controlled state,approximately 0.38 mm in a passive-off control, approxi-mately 0.23 mm in a passive-on control, approximately0.20 mm in a Lyapunov control, and approximately 0.18 mmin a clipped-optimal control. When these are represented asRMS displacement (J2), they are shown to be approximately78.11% in a passive-off control, approximately 46.93% in apassive-on control, approximately 40.83% in a Lyapunovcontrol, and approximately 36.53% in a clipped-optimalcontrol with the non-controlled state as the standard. As for

the control effects in relation to these figures, effects ofvibration size reduction were as much as approximately21.89% in a passive-off control, approximately 53.07% in apassive-on control, approximately 59.17% in a Lyapunovcontrol, and approximately 63.47% in a clipped-optimalcontrol with the non-controlled state as the standard.

6.3. Evaluation of absolute maximum acceleration

When we examine table 10 in relation to the maximumacceleration generated for each experimental condition, theresults were approximately 0.43 g in a non-controlled state,approximately 0.37 g in a passive-off control, approximately0.31 g in a passive-on control, approximately 0.27 g in aLyapunov control, and approximately 0.28 g in a clipped-optimal control. When these are represented as absolutemaximum acceleration (J3), they are shown to be approxi-mately 87.68% in a passive-off control, approximately72.24% in a passive-on control, approximately 64.84% in aLyapunov control, and approximately 65.19% in a clipped-optimal control with the non-controlled state as the standard.As for the control effects in relation to these figures, effects ofvibration size reduction were as much as approximately12.32% in a passive-off control, approximately 27.76% in apassive-on control, approximately 35.16% in a Lyapunovcontrol, and approximately 34.81% in a clipped-optimalcontrol with the non-controlled state as the standard.

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Figure 14. Simulink to clipped-optimal control.

6.4. Evaluation of RMS acceleration

When we examine table 10 in relation to the generation RMSacceleration for each experimental condition, the results wereapproximately 0.06 g in a non-controlled state, approximately0.05 g in a passive-off control, approximately 0.03 g in apassive-on control, approximately 0.03 g in a Lyapunovcontrol, and approximately 0.03 g in a clipped-optimal con-trol. When these are represented as RMS acceleration (J4),they are shown to be approximately 83.18% in a passive-offcontrol, approximately 56.39% in a passive-on control,approximately 50.59% in a Lyapunov control, and approxi-mately 52.82% in a clipped-optimal control with the non-controlled state as the standard. As for the control effects inrelation to these figures, effects of vibration size reductionwere as much as approximately 16.82% in a passive-offcontrol, approximately 43.61% in a passive-on control,approximately 49.41% in a Lyapunov control, and approxi-mately 47.18% in a clipped-optimal control with the non-controlled state as the standard.

6.5. Evaluation of input voltage

The input voltage consumption (J5) evaluated in this paper asthe vibration control performance index was calculated as theratio of input voltage consumption for each semi-activecontrol method to input voltage consumption during thepassive-on control. Table 10 shows that the number of sam-ples of input voltage consumed for each semi-active controlmethod is 2348 for the Lyapunov control and 2398 for theclipped optimal. When these are represented as input voltageconsumption (J5), the results are shown to be 46.59% in aLyapunov control, and 47.96% in a clipped-optimal controlwith the passive-on control as the standard. As for the controleffects in relation to these figures, effects were as much as53.04% in a Lyapunov control and 52.04% in a clipped-optimal control with the passive-on control as the standard.

As from the above results, in comparison with theresponse reduction performance of the two semi-active con-trol methods considered in this paper, however, the number ofsamples of output signals required for vibration control wasreduced to 53.04% in Lyapunov control and to 52.04% in

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Figure 15. Simulation of Lyapunov and clipped-optimal control algorithms. (a) Lyapunov control simulation results. (b) Clipped-optimalcontrol simulation results.

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Figure 16. Setup of semi-active vibration control test.

Figure 17. Setup of semi-active vibration control test. (a) Example of vertical vibration control. (b) Mechanism of vertical vibration control.

Figure 18. Displacement and acceleration of Lyapunov control. (a) Compare with displacement. (b) Compare with acceleration.

clipped-optimal control respectively when compared with thepassive-on control. In addition, when the two semi-activecontrol methods considered in this paper are compared witheach other, the Lyapunov control method was evaluated toshow somewhat superior control performance over the clip-ped-optimal control method in both peak and RMS responsesfor displacement; on the other hand, the clipped-optimalcontrol method was evaluated to show somewhat superiorcontrol performance over the Lyapunov control method inboth peak and RMS responses for acceleration.

7. Conclusion

After the experimental study of this paper on the control ofvertical random vibration of bridges by means of a semi-active control method based on an MR damper, the followingconclusions are made.

1. The MR damper was used to control structural vibration.It had a control power of approximately one-tenth of themaximum force, and its performance was found to besatisfactory.

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Figure 19. Displacement and acceleration of clipped-optimal control. (a) Compare with displacement. (b) Compare with acceleration.

Lyapunov control5

4.54

3.53

2.52

1.51

0.50

0 5 10 15 20 25 30 35 40 45 50

App

lied

volta

ge (V

)

Time (sec)

Figure 20. Input voltage of Lyapunov control.

54.5

43.5

32.5

21.5

10.5

00 5 10 15 20 25 30 35 40 45 50

App

lied

volta

ge (V

)

Time (sec)

Clipped-optimal control

Figure 21. Input voltage of clipped-optimal control.

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Table 10. Response, performance index, and control effect of semi-active vibration control.

Estimation results

Response Performance index Control effect

Control case

Peakdisp.(mm)

RMSdisp.(mm)

Peakaccel.(g)

RMSaccel.(g)

Inputvoltage(Sample) J1(%) J2(%) J3 (%) J4 (%) J5 (%)

Peakdisp.(%)

RMSdisp.(%)

Peakaccel.(%)

RMSaccel.(%)

Inputpower(%)

Uncontrolled 3.642 0.495 0.431 0.067 — 100 100 100 100 — 0 0 0 0 —

Passive-off 3.134 0.387 0.378 0.055 — 86.05 78.11 87.68 83.18 — 13.95 21.89 12.32 16.82 —

Passive-on 1.969 0.232 0.311 0.037 5000 54.06 46.93 72.24 56.39 100 45.94 53.07 27.76 43.61 0Lyapunov 1.722 0.202 0.279 0.034 2348 47.28 40.83 64.84 50.59 46.96 52.72 59.17 35.16 49.41 53.04Clipped 1.759 0.181 0.281 0.035 2398 48.29 36.53 65.19 52.82 47.96 51.71 63.47 34.81 47.18 52.04

2. In addition, Lyapunov and clipped-optimal controlmethods were found to be more effective in reducingdisplacement and acceleration compared with the non-controlled state than with the passive-on and passive-offcontrol methods. In particular, by comparison with thepassive-on control state, their consumption of inputvoltage was reduced to approximately 50%, whichproved these two semi-active control methods to beeconomically superior to the passive control methods.

3. Ultimately, the vibration control with shear-type MRdampers and the two semi-active control algorithmsstudied in this paper was verified to be effectivelyapplicable to any real-time semi-active vibration controlon the basis of state responses of structures; furthermore,basic data of experimental studies on real-time semi-active vibration control of bridges were provided throughthe experimental results of this paper.

4. Also, since this research is based on indoor experimentson a model structure, it should be pointed out that furtherresearch is needed to find adequate criteria to calculatethe capacity of control devices, suitable installationposition, proper numbers of control devices, developmentof control devices in various shapes and forms, designprocedure of to be systematic control algorithm, etc, andalso to conduct semi-active vibration control with MRdampers, in real time and in the field.

Acknowledgements

This research was supported by the Basic Science ResearchProgram through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science andTechnology (grant number NRF-2013R1A2A1A01016192).

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